Approximately nothing for a country
I believe the answer is:
canada
'a country' is the definition.
(Canada is an example)
'approximately nothing' is the wordplay.
'approximately' becomes 'ca' (abbreviation for circa).
'nothing' becomes 'nada' ('nada' can be a synonym of 'nothing').
'ca'+'nada'='CANADA'
'for' acts as a link.
(Other definitions for canada that I've seen before include "Part of North America" , "North American country" , "Queen Elizabeth is it's head of state" , "Second-largest country in the world by area" , "New World country" .)